"Bob has never been to Jim's house", said David Kelley, who succeeded Comey as US attorney in Manhattan and has known him and Mueller for years.
Asked point blank if Mueller should recuse himself from the Russian Federation investigation, Trump said: "Well, he's very, very good friends with Comey, which is very bothersome".
Mr Mueller has not given any details of his investigation but USA media have reported he is investigating Mr Trump for possible obstruction of justice, both in the firing of Mr Comey and whether Mr Trump tried to end an inquiry into sacked national security adviser Michael Flynn. But his arrogant and reckless firing of Comey, along with his attempts to control the investigation by former FBI Director Robert Mueller, could ultimately prove to be Trump's downfall.
Rosenstein has jurisdiction over Mueller's investigation because Attorney General Jeff Sessions, the first Republican senator to endorse Trump in the 2016 campaign, has recused himself from matters related to the campaign and Russian Federation.
BBC reports his interview with Fox & Friends on Friday, where Trump is quoted as saying "there has been no obstruction".
This is not the first time that Trump has suggested he has been surveilled without providing evidence.
Dershowitz said, however, that he's not sure Trump's tweet was a good idea because it led Comey to leak his memos and it prompted Mueller to be appointed as special counsel. The Washington Post has also reported that Mueller is investigating whether Trump attempted to obstruct the investigation.
Speculations were provoked when Trump sacked Comey, leading to controversies. Trump's new argument is that Comey told the truth under oath, but only because the president - the strategic mastermind that he is - tricked him by publishing a deceptive tweet about tapes that don't exist.
On 16 June, Mr Trump sent out a tweet appearing to accept he was under investigation, although later his aides suggested that was not the intention.
Comey's firing led to the appointment of Robert Mueller to head up the feds' Russian Federation investigation - a move that enraged the president, who has slammed the probe as a "witch hunt", "hoax" and "fake news".
Trump's claim was preposterous to Secret Service veterans, one of whom tells PEOPLE that the Secret Service's Technical Security Division regularly sweeps the Oval Office for listening devices and anything else that might have been not-so-innocently left behind by any of the president's visitors. He has many connections both inside the White House and the intelligence community, and his sources have proven to be correct in the past. I can tell you that.
After the tweet, Mr Comey testified before the Senate Intelligence Committee to make his account of interactions with the President public. "I can say that the people who have been hired are all Hillary Clinton supporters". Those days came and went without an answer.
Robert Mueller, the somber-faced and demanding FBI director who led the bureau through the September 11 attacks, and James Comey, his more approachable and outwardly affable successor, may be poles apart stylistically but both command a wealth of respect in the law enforcement and legal community.
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